A Computational Protocol for Vibrational Circular Dichroism Spectra of Cyclic Oligopeptides

Cyclic peptides are a promising class of compounds for next-generation antibiotics as they may provide new ways of limiting antibiotic resistance development. Although their cyclic structure will introduce some rigidity, their conformational space is large and they usually have multiple chiral centers that give rise to a wide range of possible stereoisomers. Chiroptical spectroscopies such as vibrational circular dichroism (VCD) are used to assign stereochemistry and discriminate enantiomers of chiral molecules, often in combination with electronic structure methods. The reliable determination of the absolute configuration of cyclic peptides will require robust computational methods than can identify all significant conformers and their relative population and reliably assign their stereochemistry from their chiroptical spectra by comparison with ab initio calculated spectra. We here present a computational protocol for the accurate calculation of the VCD spectra of a series of flexible cyclic oligopeptides. The protocol builds on the Conformer-Rotamer Ensemble Sampling Tool (CREST) developed by Grimme and co-workers (Phys. Chem. Chem. Phys.2020, 22, 7169−719232073075 and J. Chem. Theory. Comput.2019, 15, 2847–286230943025) in combination with postoptimizations using B3LYP and moderately sized basis sets. Our recommended computational protocol for the computation of VCD spectra of cyclic oligopeptides consists of three steps: (1) conformational sampling with CREST and tight-binding density functional theory (xTB); (2) energy ranking based on single-point energy calculations as well as geometry optimization and VCD calculations of conformers that are within 2.5 kcal/mol of the most stable conformer using B3LYP/6-31+G*/CPCM; and (3) VCD spectra generation based on Boltzmann weighting with Gibbs free energies. Our protocol provides a feasible basis for generating VCD spectra also for larger cyclic peptides of biological/pharmaceutical interest and can thus be used to investigate promising compounds for next-generation antibiotics.


Molecule 1a
Molecule 2a  S-3 (6-31+G) are qualitatively different to all other calculated spectra ( Figure S1, top). This observation is confirmed by the overlap estimates in Table S1, which increase from 0.26 to 0.44 for 1a and from 0.30 to 0.80 for 2a upon the addition of the first set of polarization functions. The overlap estimates using 6-31+G*, 6-31++G* and 6-311+G* for 1a are rather low for both the IR and VCD spectra compared to 2a. This is due to changes in the frequency gap between the amide I and amide II regions. In fact, the frequencies in the amide I region for the three basis sets agree well with the spectrum calculated with 6-311++G**, whereas there is a small shift towards lower frequencies in the range 1600-1100 cm −1 ( Figure S3).
Bour et al. found that the VCD band shape of a cyclic hexapeptide was in general very similar using 6-311++G** and 6-31G**, but that 6-311++G** provided slightly lower frequencies. This was most pronounced in the amide I region, and the addition of diffuse functions led to better agreement with experiment. S2 The latter observation is in agreement with our results (bottom row Figure S1). Indeed, especially the first set of diffuse functions leads to a decrease of the frequency gap between the amide I and amide II regions and hence to a better agreement with experiment.
Changing the basis set from 6-31+G* to 6-311++G** for 1a and 2a, however, leads to an increase in the number of basis functions from 420 to 580 and 676 to 930, respectively, for 1a and 2a. Since 6-31+G* gives qualitatively similar spectra to 6-31++G*, 6-31+G** and 6-311+G*, we conclude that this basis set is a good compromise between accuracy and computational efficiency. This is particularly important as our longer-term goal is to investigate much larger peptides. For this reason, the 6-31+G* basis set will be used in the remainder of this paper.

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Scaling factor Figure S4: IR and VCD spectra of molecules 1a (left) and 2a (right) with different scaling factor f for the calculated (B3LYP/6-31+G*/CPCM) spectra, compared with experiment. Table S2: Overlap estimate S between calculated and experimental IR and VCD spectra using different scaling factor f . S is calculated over the frequency range shown i Figure S4: 1800-1500 cm −1 for 1a and 1800-1100 cm −1 for 2a.

Molecule 1a
Molecule 2a  The effect of using different frequency scaling factors on the spectra for 1a and 2a are shown in Figure S4 (IR and VCD spectra) and Table S2 (overlap estimates S). The two molecules show the same trends when it comes to scaling factor, with the overlap estimate for both the IR and VCD spectra going through a maximum for a scaling factor of 0.98.
Merrick, Moran and Radom recommended a scaling factor for B3LYP/6-31+G* of 0.9636 based on a comparison with experimental gas-phase data. S1 Our calculations for 1a and 2a

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have instead been compared to solution spectra using respectively trifluoroethyl alcohol (TFE) and acetonitrile (ACN) as solvents, and shows that scaling the frequencies by 0.96 gives poor agreement with experiment, both quantitatively ( Figure S4) and qualitatively (Table S2). Indeed, the negative S-values for the VCD spectra indicate that the calculated VCD spectra have more spectral overlap with the enantiomer of the investigated molecules.
A scaling factor of 0.98 gives the best agreement between the calculated and experimental spectra for both molecules (Table S2). Poor agreement between experimental and calculated spectra using gas-phase fitted scaling factors has also been previously noted for solvated systems. S4-S6 We note, however, that peptides pose a particular challenge when comparing to experiment, as the amide I-II gap cannot be reliably reproduced without taking solutesolvent interactions explicitly into account, and the scaling factor thus becomes a compromise in our description of these important bands. S2 Whenever comparing to experimental spectra, the frequencies are scaled with the factor giving the largest overlap estimate S between the calculated and experimental spectra.

S-7
Enthalpies and Gibbs free energies in the Boltzmann weight  Figure S5: Calculated VCD spectra of 2a, 2b, 2c and 3 with free energies (∆G, red) and entalpies (∆H, green) in the Boltzmann weights. The calculations are done with B3LYP, 6-31+G* and CPCM.